Folding a small protein using harmonic linear discriminant analysis.

Many processes of scientific importance are characterized by time scales that extend far beyond the reach of standard simulation techniques. To circumvent this impediment, a plethora of enhanced sampling methods has been developed. One important class of such methods relies on the application of a bias that is a function of a set of collective variables specially designed for the problem under consideration. The design of good collective variables can be challenging and thereby constitutes the main bottle neck in the application of these methods. To address this problem, recently we have introduced Harmonic Linear Discriminant Analysis, a method to systematically construct collective variables as linear combinations of a set of descriptors. The method uses input information that can be gathered in short unbiased molecular dynamics simulations in which the system is trapped in the metastable states. Here, to scale up our examination of the method's efficiency, we applied it to the folding of chignolin in water. Interestingly, already before any biased simulations were run, the constructed one-dimensional collective variable revealed much of the physics that underlies the folding process. In addition, using it in metadynamics, we were able to run simulations in which the system goes from the folded state to the unfolded one and back, where to get fully converged results, we combined metadynamics with parallel tempering. Finally, we examined how the collective variable performs when different sets of descriptors are used in its construction.